System and Method of Word Graph Matrix Decomposition

1. A method of generating a block diagonal matrix from a lattice, the method comprising: (1) if a lattice having transitions T is weighted, computing posterior probabilities of all transitions T in a graph; (2) extracting a pivot baseline path from the lattice; and (3) aligning the transitions T in the lattice with the transitions in the pivot baseline path.

2. A method of claim 1 , wherein the graph is a word graph.

3. The method of claim 2 , wherein aligning the transitions T further comprises, for all transitions T in the topologically ordered lattice, performing the following: A. using time slots of transitions T, finding the most overlapping location on the pivot baseline; B. if there is no transition at that location that precedes T in the lattice, performing the following: i. if a transition with the same label already occurs at that location, adding posterior probability of T to the posterior probability of that transition; ii. if a transition with the same label does not already occur at that location, inserting a new transition to that location with the label and posterior probability of T; C. if there is a transition at that location that precedes T in the lattice, performing the following: i. inserting a new state S n to the pivot alignment; ii. assigning that state a time information; iii. changing the destination state of all transitions originating from state S s to S n ; and iv. inserting a transition between states S n and S e and assigning it the label and posterior of T, wherein the lattice is transformed into a block diagonal matrix.

4. The method of claim 3 , wherein computing posterior probabilities of all transitions T in a word graph further comprises performing a forward and a backward pass through the word graph.

5. The method of claim 3 , wherein if the lattice is not weighted, skipping the step of computing posterior probabilities of all transitions.

6. The method of claim 3 , wherein extracting the pivot baseline path further comprises extracting the best path from the lattice.

7. The method of claim 3 , wherein extracting the pivot baseline path further comprises extracting the longest path from the lattice.

8. The method of claim 1 , wherein extracting the pivot baseline path further comprises extracting a random path from the lattice.

9. The method of claim 3 , wherein the time slots of transition T comprise a speech interval between starting and ending time frames of T.

10. The method of claim 1 , wherein the block diagonal matrix is smaller in size than the lattice.

11. The method of claim 1 , wherein the block diagonal matrix has the computational property.

12. The method of claim 1 , wherein if the lattice is weighted, the method further comprises using the probabilities of the block diagonal matrix as word confidence scores.

13. The method of claim 1 , wherein the method further comprises using the probabilities of the most probable path of the block diagonal matrix as confidence scores for unsupervised learning of language models.

14. The method of claim 1 , wherein the method further comprises using the probabilities of the most probable path of the block diagonal matrix as confidence scores for unsupervised learning for automatic speech recognition.

15. The method of claim 3 , wherein the method further comprises applying the probabilities of the block diagonal matrix confidence scores to spoken language understanding.

16. The method of claim 3 , wherein the method further comprises applying the probabilities of the block diagonal matrix confidence scores to machine translation.

17. The method of claim 3 , wherein the method further comprises applying the probabilities of the block diagonal matrix confidence scores to named entity extraction.

18. The method of claim 1 , wherein the block diagonal matrix is smaller in size than the lattice.

19. A method of linearizing a lattice, the method comprising: (1) if a lattice having transitions T is weighted, computing posterior probabilities of all transitions T in a graph; (2) extracting a pivot baseline path from the lattice; and (3) linearizing the lattice by aligning the transitions T in the lattice with the transitions in the pivot baseline path, wherein the linearized lattice can be visualized.